apaulus4907
Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

The height of a model rocket, [tex]H(t)[/tex], is a function of the time since it was launched, [tex]t[/tex].

What is the domain of [tex]H(t)[/tex]?

A. [tex]t \leq 225[/tex]
B. [tex]0 \leq t \leq 30[/tex]
C. [tex]0 \leq t \leq 225[/tex]
D. [tex]t \geq 0[/tex]

Sagot :

GinnyAnswer
To determine the domain of the height function of a model rocket, [tex]\( H(t) \)[/tex], we need to think about the physical context of the problem. The domain of the function represents the set of all possible values of [tex]\( t \)[/tex] for which the function [tex]\( H(t) \)[/tex] is defined, where [tex]\( t \)[/tex] represents the time since the rocket was launched.

Here's a breakdown of how we can determine this:

1. Understanding the Context: The height [tex]\( H(t) \)[/tex] will be defined starting from the moment the rocket is launched (time [tex]\( t = 0 \)[/tex]) until the moment it hits the ground or finishes its trajectory. Before launch, [tex]\( t \)[/tex] would be irrelevant ([tex]\( t < 0 \)[/tex] doesn't make sense), and after it hits the ground, the height can be assumed to be [tex]\( 0 \)[/tex], meaning the function [tex]\( H(t) \)[/tex] has no further meaningful values.

2. Inspecting the Given Options:
- A. [tex]\( t \leq 225 \)[/tex]: This says the function is defined for all times less than or equal to 225 seconds, but it doesn't specify a starting point. [tex]\( t \)[/tex] could theoretically go to negative values, which physically doesn't make sense in this context.
- B. [tex]\( 0 \leq t \leq 30 \)[/tex]: This limits the time to at most 30 seconds, which might not encapsulate the entire flight duration of the rocket.
- C. [tex]\( 0 \leq t \leq 225 \)[/tex]: This one specifies that the time ranges from launch ([tex]\( t = 0 \)[/tex]) to some maximum flight time (up to [tex]\( t = 225 \)[/tex] seconds), which seems reasonable for a complete flight trajectory.
- D. [tex]\( t \geq 0 \)[/tex]: This suggests the height is defined for all time [tex]\( t \)[/tex] greater than or equal to 0, theoretically extending to infinity, which isn't practical since the rocket follows a finite flight path.

3. Choosing the Best Option: For a model rocket, we would typically expect it to have a launch, a peak, and then a descent until it lands back to the ground. Given the choices, the duration that seems to correctly reflect the flight of a model rocket from launch to landing is option C. [tex]\( 0 \leq t \leq 225 \)[/tex].

Thus, the domain of [tex]\( H(t) \)[/tex] is best represented by option C. [tex]\( 0 \leq t \leq 225 \)[/tex].
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.